Molecular dynamics simulations of fluorine molecules interacting
with a Siˆ100‰(231) surface at 1000 K
T. A. Schoolcrafta) and A. M. Diehl
Department of Chemistry, Shippensburg University, Shippensburg, Pennsylvania 17257
A. B. Steelb)
Department of Chemistry, Gettysburg College, Gettysburg, Pennsylvania 17325
B. J. Garrisonc)
Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802
~Received 22 April 1994; accepted 11 March 1995!
Molecular dynamics simulations are performed to examine the adsorption of fluorine molecules,
having incident translational kinetic energies between 0.0195 and 1.67 eV, on a clean Si$100%~231!
surface at 1000 K. Results using the Stillinger and Weber potential energy function and the
Weakliem, Wu, and Carter parameterization of this potential energy function are compared to each
other and to experimental results. The initial sticking probability increases as the incident kinetic
energy increases. As the incident kinetic energy increases, more difluorination and less
monofluorination is observed as barriers to adsorption are overcome. For difluorination, a time delay
between the two atom adsorption events is quantified. © 1995 American Vacuum Society.
I. INTRODUCTION
The adsorption of fluorine molecules on a clean
Si$100%~231! surface is fundamentally different from the adsorption of fluorine atoms. In progressing from atomic fluorine to molecular fluorine, the addition of only one more
atom and thus a bond, increases the number of possible reaction results. When fluorine atoms interact with the clean
Si$100%~231! surface, the atoms can be either repelled or
adsorbed.1 When F2 molecules interact with the clean silicon
surface, there are three possible results.2–5 In one case, the F2
molecule repels from the surface, i.e., no chemical reaction
occurs. Another possible result is for the F–F bond to break
and one Si–F bond to form with the other fluorine atom
ejecting into the vacuum, i.e., monofluorination or atom abstraction. The possible final outcome is for the F–F bond to
break and two Si–F bonds to form, i.e., difluorination. Difluorination, generically known as dissociative chemisorption,
is generally believed to occur via one of two mechanisms.6
The first mechanism is direct adsorption. When the F2 molecule adsorbs, the F–F bond breaks immediately upon the
molecule’s interaction with the surface and two Si–F bonds
form. As the incident kinetic energy increases, this mechanism is characterized by an initial sticking probability that
increases because it is easier for the activation barrier to be
overcome. The second mechanism involves a molecular precursor state. Here the F–F bond does not break immediately
upon the molecule’s initial interaction with the surface. The
molecule loses sufficient translational kinetic energy and becomes physisorbed to the surface. The physisorbed molecule
then reorients or diffuses in order to find a site where it can
dissociate and therefore chemisorb. The molecule can also
fail to react after spending some time physisorbed and then
a!
Electronic mail: [email protected]
Current address: Department of Chemistry, University of Maryland, College Park, MD 20742.
c!
Electronic mail: [email protected]
b!
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J. Vac. Sci. Technol. A 13(4), Jul/Aug 1995
desorb unreacted. The precursor mechanism is characterized
by an initial sticking probability that decreases as the incident kinetic energy increases because the molecule must lose
more translational energy in order to become trapped. From
this study, however, a fourth mechanism for dissociative
chemisorption is found that will be referred to as an atomic
precursor state mechanism to distinguish it from the molecular precursor state mechanism. In this scenario, one fluorine
atom of the F2 molecule chemisorbs, yet the second fluorine
atom does not adsorb or desorb immediately. The F–F bond
lengthens and the second fluorine atom reorients or diffuses
in order to find an adsorption site. If the second fluorine atom
finds a dangling bond, the end result is difluorination and, if
not, the end result is monofluorination.
Evidence of an atomic precursor state mechanism for the
dissociative chemisorption of F2 molecules on the
Si$100%~231! surface is suggested in theoretical investigations that examine this system,2,3,7 and also by several experimental investigations that examine the desorption of H2
molecules from the Si$100%~231! surface.8 –10 The first theoretical investigation is a molecular dynamics simulation performed by Weber and Stillinger.2 The authors investigated
the reaction dynamics of F2 molecules with a Si$100%~231!
surface at 0 K. Although Weber and Stillinger display trajectories where the fluorine atoms adsorb nonsimultaneously,
they do not investigate them in detail. Provided that this is
not an artifact of the potential energy function, the timestaggered adsorption suggests an atomic precursor state
mechanism. The second theoretical investigation is a SLABMINDO semi-empirical calculation performed by Craig and
Smith.7 These authors found a complexed structure when
they examined the minimized energy configuration for an
adsorbed F2 molecule on the Si$100%~231! surface. The
Si–Si dimer bond is stretched from its equilibrium length of
2.217 to 2.859 Å and the F–F bond distance is also stretched
from an equilibrium value of 1.446 to 1.610 Å. The F2 molecule is positioned over one end of the dimer pair so that one
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©1995 American Vacuum Society
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Schoolcraft et al.: Molecular dynammics simulations of F molecules
fluorine atom is almost vertical above a silicon atom and the
other fluorine atom is almost directly above the dimer bridge
site. The Si–F bond lengths are 1.615 and 1.618 Å. Although
this configuration differs from the Si–F•••F complex formation observed by Weber and Stillinger,2 it also suggests a
precursor structure to adsorption. Additional support is found
in molecular hydrogen desorption studies.8,9 After several investigations, the unusual first-order recombinative behavior
of hydrogen desorption from the Si$100%~231! surface was
explained as being due to preferential pairing of the hydrogen adatoms on the surface.10–12 In order for H2 to desorb,
each silicon of a dimer pair must be a monohydride species.
Next, one hydrogen of the pair migrates toward the other
monohydride species to form a dihydride species. Once this
species is formed, the H2 desorbs leaving behind an unoccupied dimer pair. This desorption behavior explains the low
initial reaction probability of H2 with the Si$100%~231! surface. Only silicon atoms which have two dangling bonds can
be adsorption sites and these sites are not very numerous on
this surface.
The silicon/fluorine potential energy function was developed by Stillinger and Weber ~SW!.2,13–15 Weakliem, Wu,
and Carter ~WWC!, finding the Stillinger and Weber potential to be too repulsive for fluorine atom adsorption on the
Si$100%~231! surface, have reparameterized only the Si–F
portion to fit electronic structure calculations of fluorine
atom adsorption on Si$100%~231!.16,17 These researchers
have performed similar calculations as Stillinger and Weber
for a 298 K surface instead of a 0 K surface using both the
SW potential and the WWC parameterization.3,18 Since the
experimental investigations by Ceyer and co-workers5 were
performed at 1000 K, this article re-examines the reaction
pathways of this system at this experimental temperature using the SW potential and WWC parameterization.
II. DESCRIPTION OF THE SIMULATION
Molecular dynamics calculations are performed for the
scattering of F2 molecules from a clean Si$100%~231! surface
maintained at 1000 K using both the SW silicon/fluorine potential and the WWC parameterization. The temperature of
1000 K is chosen as the experiments of Ceyer et al. were
performed at this temperature.5 The silicon crystal consists of
320 atoms where the details of this crystal are described
elsewhere in an article describing the spontaneous etching of
Si by reaction with F atoms.19 For the purpose of investigating the dependence of the sticking probability on the incident
kinetic energy of the F2 molecule, three different kinetic energies for the fluorine molecules are used: 0.0195, 0.234, and
1.67 eV. The energy of 0.234 eV or 5.4 kcal/mol is the same
as used in the simulations at the lower surface
temperatures.2,3 For each incident kinetic energy, 200 trajectories are performed.
To simplify the analysis of a trajectory, the fluorine molecule possesses neither rotational nor vibrational energy, thus
all incident kinetic energy is purely translational. The center
of mass of the molecule is normally incident and is aimed in
a region on the surface that represents the entire surface due
to symmetry.1 The height, z, of the center of mass is initially
4.7 Å above the surface. This height places the fluorine molJ. Vac. Sci. Technol. A, Vol. 13, No. 4, Jul/Aug 1995
1862
TABLE I. The number of different trajectory classifications for parameterization and for each incident kinetic energy.
0.0195 eV
Difluorination
Monofluorination
Nonreactive
Complex
S0
0.234 eV
1.67 eV
WWC
SW
WWC
SW
WWC
SW
45
155
0
0
0.61
34
140
19
7
0.54
103
97
0
0
0.76
57
139
3
1
0.64
172
28
0
0
0.93
112
83
5
0
0.77
ecule sufficiently out of range of any interaction with the
surface. Before each deposition event, the crystal’s motion is
integrated for a random time interval between zero and
;1250 fs ~1 fs51310215 s!, thus allowing the crystal to be
in a random vibrational phase for each trajectory of the incoming fluorine molecule. The orientation of the molecule is
generated randomly where the azimuthal angle, F, is chosen
between 0° and 180°, and the polar angle, Q, is chosen such
that cosine Q is between 0 and 1.20
The result of each trajectory is placed into one of the four
categories first observed by Weber and Stillinger:2 difluorination, monofluorination or atom abstraction, repulsion and
complex formation. Difluorination is determined when the
total energy of each fluorine atom is ;25 eV. This indicates
that two Si–F bonds have formed since the Si–F bond energy is ;5–7 eV depending upon the parameters in the potential. For comparison, the F–F bond energy is ;1.6 eV and
the Si–Si bond energy is ;2–3 eV. Monofluorination is determined when the total energy of one of the fluorine atoms
is ;25 eV, and the potential energy of the other fluorine
atom is zero and its z component of the velocity is directed
away from the surface. Repulsion is determined when the z
coordinate of both of the fluorine atoms passes a plane ;8.4
Å above the surface, the z components of both velocity vectors are directed away from the surface, and the fluorine
atoms still form a molecule. Complex formation is defined
when the total energy of one fluorine atom is;25 eV, the
total energy of the other fluorine atom is between 21 eV and
zero, and ;5 picoseconds ~ps! have passed in the simulation.
No trajectories formed complexes with the WWC parameterization using 5 ps as a cutoff time to end a trajectory, unlike
trajectories calculated using the SW potential. We did not
observe trajectories in which both F atoms desorbed as
atoms.
III. RESULTS AND DISCUSSION
The number of each different type of trajectory ~difluorination, monofluorination, nonreactive and complex formation! for each parameterization and for each incident kinetic
energy is summarized in Table I. At all incident energies the
major reaction channels are difluorination and monofluorination with difluorination more predominant at the higher kinetic energies. For the SW potential there are a small amount
of trajectories which do not react and a few trajectories in
which complexes are formed. In contrast, the simulations at
lower temperatures2,3 have much larger percentages of trajectories ~6%–13% at 0.234 eV! in which there is complex
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Schoolcraft et al.: Molecular dynammics simulations of F molecules
FIG. 1. Kinetic energy distribution of the ejected fluorine atoms for monofluorination events. The distributions are individually peak normalized.
formation, an observation independent of parameterization.
For the lower surface temperature the SW potential predicts
nonreactive yields of 16%– 45%, a value considerably higher
than found in these investigations. Likewise, the lower surface temperature simulations show a lower percentage of difluorination relative to monofluorination trajectories. In summary, the higher surface temperature almost eliminates
nonreactive and complex formation events. It also enhances
difluorination relative to monofluorination.
The two experimental values of the initial sticking probability are by Engstrom et al.21 and Ceyer et al.5 Engstrom
reports a value of 0.46 with Ceyer’s value approximately
0.83. In the calculations the initial sticking probability, S 0 , is
determined by multiplying the number of difluorination trajectories by two and adding this number to the number of
monofluorination and complex formation trajectories and
then dividing this sum by twice the total number of trajectories. Since Ceyer’s experiments are performed at energies
nearer the lower two energy values given in Table I, it appears that the calculated sticking probabilities fall midway
between the experimental values. The disturbing feature is
that Ceyer finds that the majority ~;90%!5 of the sticking
events are difluorination, whereas both the SW potential and
the WWC parameterization underestimate the amount of difluorination. Two possibilities for the discrepancy come to
mind. First, the activation energy for difluorination could be
JVST A - Vacuum, Surfaces, and Films
1863
FIG. 2. Polar angle of the ejecting fluorine atom for monofluorination events
where 0° is ejection perpendicular to the surface plane and 90° is ejection
parallel to the surface plane. The distributions are counted in steps of 10°,
are weighted for hemispherical collection, and are peak normalized. The
legend is the same as in Fig. 1.
too large since the Si–F–F interaction is too repulsive.3 Second, the potential should be longer ranged. This potential and
most others for Si are limited to nearest-neighbor interactions. If the real interaction is longer ranged then, after the
first fluorination event, the second F atom would be pulled
closer to the surface.
The ejected fluorine atoms from the monofluorinated
events are analyzed as to their kinetic energy of ejection
~Fig. 1! and their polar angle of ejection ~Fig. 2!. One striking observation in the kinetic energy distributions is that the
shapes of the distributions are similar, i.e., the distributions
are not strongly dependent on the initial conditions or parameterization and thus must be a function of the adsorption
process. Another observation is that the distributions peak in
roughly the same kinetic energy range, 0.25–0.45 eV, even
though two of the three incident kinetic energies are below
these peak values. Carter et al. also observe these same results with a 298 K crystal.3 Interestingly, the shapes of the
polar distributions ~Fig. 2! are similar to each other also and
are almost ‘‘cosine-like,’’ thus, there is no preferred angle of
ejection. Once again, this indicates that the atom abstraction
event is independent of the initial conditions of the fluorine
molecule.
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Schoolcraft et al.: Molecular dynammics simulations of F molecules
1864
TABLE III. The number of each pattern of difluorination for the SW potential
and the percentage of the trajectories that had nonsimultaneous adsorption.
A total of 200 trajectories were performed at each incident energy. See Fig.
3 for the pattern classifications.
0.0195 eV
FIG. 3. Difluorination patterns: ~a! opposing, ~b! vicinal, ~c! diagonal, ~d!
vicinal once-removed, ~e! opposing once-removed, ~f! diagonal along the
row, ~g! diagonal along the row once-removed, ~h! diagonal across the
trough once-removed, and ~i! same dimer pair.
The trajectories where both fluorine atoms adsorb to silicon dimer atoms are analyzed as to the patterns of adsorption
that result on the surface ~Fig. 3! and the probability of adsorption ~Tables II and III!. Where appropriate, the results in
this section are compared to the molecular dynamics results
of Weber and Stillinger with a 0 K crystal2 and to the results
of Carter et al. with a 298 K crystal.3 Figures 3~a!–3~i! depict nine of the 11 observed difluorination patterns that are
observed in the simulation where the first three patterns are
TABLE II. The number of each pattern of difluorination for the WWC parameterization and the percentage of the trajectories that had nonsimultaneous adsorption. A total of 200 trajectories were performed at each incident
energy. See Fig. 3 for the pattern classifications.
0.0195 eV
Opposing Fig. 3~a!
Vicinal Fig. 3~b!
Diagonal Fig. 3~c!
SiF2
Second layer
Figure 3~d!
Figure 3~e!
Figure 3~f!
Figure 3~g!
Figure 3~h!
Figure 3~i!
25
7
4
4
1
2
1
0
0
0
0
40%
17%
50%
25%
0%
0%
100%
Total
44
34%
0.234 eV
54
24
11
2
3
1
2
3
1
2
0
28%
33%
36%
0%
33%
100%
0%
33%
100%
100%
103
32%
J. Vac. Sci. Technol. A, Vol. 13, No. 4, Jul/Aug 1995
1.67 eV
55
53
19
7
15
3
11
7
0
0
2
27%
26%
37%
14%
40%
33%
27%
0%
100%
172
29%
Opposing Fig. 3~a!
Vicinal Fig. 3~b!, II
Diagonal Fig. 3~c!
SiF2
Second layer
Figure 3~d!
Figure 3~e!
Figure 3~f!
Figure 3~g!
Figure 3~h!
Figure 3~i!,I
21
7
2
3
0
0
0
1
0
0
0
100%
100%
100%
100%
Total
34
100%
100%
0.234 eV
1.67 eV
27
13
11
1
1
1
0
2
0
0
1
26%
23%
18%
0%
0%
100%
100%
84%
100%
80%
100%
100%
100%
34
37
16
10
11
1
0
0
0
0
3
57
28%
112
92%
100%
67%
also those observed by Weber and Stillinger. Two patterns
not depicted are the formation of an SiF2 adspecies where
both fluorine atoms adsorb to the same silicon atom, and the
second layer pattern where one of the fluorine atoms adsorbs
to a second layer atom and the second fluorine atom adsorbs
to a nearby first layer or to another second layer atom. For
the SW potential ~Table III!, the temperature affects the adsorption results. Weber and Stillinger report only three difluorination patterns using a 0 K crystal whereas these results
using a 1000 K crystal show five new difluorination patterns:
SiF2 formation, second layer sticking by one of the fluorine
atoms and patterns shown in Figs. 3~d!, 3~f!, and 3~i!. Since
SW only observed three difluorination patterns, where the
fluorine atoms adsorb near each other on the surface, they
concluded that surface diffusion plays a small role in the
adsorption process. According to our results, diffusion still
plays a small role, as is evidenced by the production of patterns such as those found in Figs. 3~d!, 3~f!, and 3~i!. The
WWC parameterization increases the probability of diffusion
a little as evidenced by the new observed difluorination patterns @Figs. 3~e!, 3~g!, and 3~h!#. For both parameterizations,
the Si–F cutoff value is the same, 3.76 Å, thus the increase
in the number of diffusion induced patterns using the WWC
parameterization must be a result of the increase in the overall attraction of the fluorine atom to the silicon surface.
Adsorption patterns have been measured for low energy
Cl2 adsorption onto Si$001%~231!.22 Boland finds that the
dominant adsorption patterns are Figs. 3~i! and 3~b!, his type
I and II respectively, although he does not give the relative
contribution of each. This is in contrast to the calculated
results in which the opposing adsorption pattern @Fig. 3~a!
dominates at low adsorption energies. Without further data it
is impossible to ascertain whether this difference is due to
deficiencies in the potential, a difference between F and Cl,
or equilibration in the experimental data.
In order to investigate the role of time-staggered adsorption in difluorination events, the time between the adsorption
of each fluorine atom was calculated. This was accomplished
by recording the time in the simulation when the potential
energy of each fluorine atom was less than 25 eV. Changing
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Schoolcraft et al.: Molecular dynammics simulations of F molecules
FIG. 4. Distribution of the amount of time between the adsorption of each
fluorine atom of the molecule for difluorination events. All distributions are
peak normalized.
this criterion to a smaller potential energy does not significantly change the calculated adsorption time difference. Figure 4 shows the distribution of the time differences of difluorination for each initial condition. Regardless of the
parameterization, time-staggered adsorption is observed thus
giving more indication that some molecules adsorb via an
atomic precursor mechanism. In addition, the amount of time
between the adsorption of the fluorine atoms decreases as the
incident kinetic energy of the molecules increases, i.e., more
molecules adsorb via the direct adsorption mechanism. This
increase in the incident kinetic energy makes a dramatic difference in the distribution of the fluorine atom adsorption
time difference using the SW potential and makes little difference using the WWC parameterization. As expected, the
WWC parameterization shows fewer overall time-staggered
adsorptions than does the SW potential. This time-staggered
adsorption mechanism is implied by Carter.3 While they do
not report quantitative results for the amount of time between
adsorption events or for the percentage of adsorption events
that occur in this manner, they do verify that this mechanism
is due to poor placement of the second fluorine atom over
low reactivity sites, such as over a Si–Si surface dimer bond.
One interesting question to ponder is the reverse reaction,
F2 desorption. Although this is highly improbable given the
relative energetics of the Si–F bond strength and the F2 bond
JVST A - Vacuum, Surfaces, and Films
1865
strength, such a process does occur for H on Si. Most models
for desorption assume that the two H atoms are originally
near each other. Given that we observe dissociative adsorption events with the atoms several sites apart, and that there
can be relatively long times between the adsorption events, is
the reverse process feasible. That is, can one atom attain a
precursor position and later find a partner?
Tables II and III detail the percentage of the difluorination
trajectories whose fluorine atoms do not adsorb simultaneously, i.e., the difference in the time of adsorption for each
fluorine atom is greater than 7.65 fs, which is the arbitrary
time increment used to output data during a trajectory. This
information shows a dramatic difference between the two
parameterizations. In general, nearly all of the difluorination
trajectories using the SW potential occur nonsimultaneously,
whereas only one-third of those using the WWC parameterization occur nonsimultaneously.
The dependence of difluorination on the initial polar and
azimuthal angles of the molecular bond was investigated.
Not surprisingly, as the initial kinetic energy of the F2 molecule increases, molecules whose bond axis is perpendicular
to the surface are less likely to difluorinate. Conversely, the
more parallel the bond axis is to the surface, the more likely
the molecule is to difluorinate as the incident kinetic energy
increases. The importance of orientation is seen also by
Carter and co-workers.18 All azimuthal angles contribute
nearly equally to difluorination for the molecules with the
highest incident kinetic energy, whereas at the lowest incident kinetic energy, the azimuthal angles that are closer to
being perpendicular to the silicon–silicon surface dimer
bond are less likely to difluorinate. For nonsimultaneous difluorination trajectories, there does not appear to be a dependence regarding the molecule’s initial polar angle. There is,
however, a general trend for there to be more time-staggered
adsorption mechanisms for molecules whose bonds are perpendicular to the dimer bond than parallel.
IV. CONCLUSIONS
Molecular dynamics simulations were performed to investigate how fluorine molecules react with a clean
Si$100%~231! surface at 1000 K. Stillinger and Weber’s
~SW! Si–F potential and the Weakliem, Wu and Carter
~WWC! reparameterization of the Si–F portion were used.
Using the SW potential, the end result of a trajectory is difluorination, monofluorination, repulsion or complex formation, whereas only difluorination or monofluorination are observed using the WWC parameterization. The experiments of
Ceyer5 predict some repulsion in contrast to the predictions
using the WWC parameterization. Both the SW potential and
the WWC parameterization predict less difluorination than
observed by Ceyer. Since this is the most specific piece of
experimental data, it is discouraging that both parameterizations of the SW potential fail to predict the high amount of
difluorination. In fact, it is not possible from the available
experimental data to make a clear determination of which
potential is better. Upon analysis of the ejected fluorine atoms of monofluorination events, we find that the adsorption
of the first fluorine atom of the diatomic molecule is inde-
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Schoolcraft et al.: Molecular dynammics simulations of F molecules
pendent of both the incident kinetic energy and the parameterization. The adsorption of the second fluorine atom, however, is sensitive to these two variables because it can adsorb
simultaneously with the first fluorine atom or within an average time of 50 fs, thus via an atomic precursor mechanism.
The SW potential predicts more atomic precursor mediated
trajectories than the WWC parameterization and the time between adsorption events for the SW potential is longer than
for the WWC parameterization. In addition, the WWC parameterization produces a larger variety of diffusion induced
difluorination adsorption patterns, providing additional support for the idea of an atomic precursor mediated mechanism
for the adsorption of molecular fluorine. It is important to
note that these empirical potential energy functions are not fit
to the observed time-staggered adsorption mechanism. This
mechanism is due to the configuration of the second fluorine
atom with the surface once the first fluorine atom has adsorbed. If the second fluorine atom is not close enough to a
dangling bond to feel its strong attraction and if it does not
possess enough kinetic energy to break its weak attraction to
the adsorbed fluorine adatom, time-staggered adsorption/
desorption is observed. The results of this article, along with
recent hydrogen desorption studies from this same surface,
suggest further mechanistic investigations of diatomic adsorption on semiconductor surfaces via experiments and ab
initio electronic structure calculations need to be performed.
ACKNOWLEDGMENTS
The authors would like to thank the Office of Naval Research for financial support and The Pennsylvania State University for the generous amount of computer time provided
to perform this work. One author ~T.A.S.! would like to ex-
J. Vac. Sci. Technol. A, Vol. 13, No. 4, Jul/Aug 1995
1866
press her sincerest gratitude to Mike Martys at Gettysburg
College for his time and support and to Gettysburg College
for computer equipment and time.
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